Thinking in 3D: Slices through cylinders

IntroductionIn geology, we often need to visualize the interior of an object or objects that we can’t observe directly. Although many people erroneously believe that 3D thinking skills are genetic (you either have them or you don’t), a preponderance of research shows that they improve with practice, just like any other skill. This exercise is designed to give you some practice thinking about slices through cylinders.

You might be asking yourself, “Why cylinders?” While perfect cylinders rarely, if ever, occur in nature, some geological objects have approximately cylindrical shapes: crinoid stems, belemnites, some kimberlite pipes, stretched pebbles in some deformed conglomerates. (Can you think of others?) In the exercises below, imagine that the cylinder shown is on of these (perhaps a crinoid stem, like the fossils in the rock photo below), and you want to be able to recognize any possible slice through it in an outcrop or a thin section.

Thomas Hickson, University of St. Thomas, and Ilyse Resnick, University of DelawareSpring, 2015

1. Match the following cylinders with the correct cross sections.

2. Describe what happens to the shape of the cut as the cutting plane changes from a dip of 0 degrees to 90 degrees, as shown in the sequence of images below.

Thomas Hickson, University of St. Thomas, and Ilyse Resnick, University of DelawareSpring, 2015

3. The following images are from cylinders that were cut by planes dipping 0 degrees, 45 degrees, 60 degrees, and 90 degrees. Label each cut with the correct angle.

4. Check your answers for question 3 by comparing them to the images in questions 1 & 2. Are they correct? Do the images in question 3 change your answer to question 2 in any way? (Modify it now if they do.)

5. Here’s an image of a cylinder sliced by a plane that dips 45 degrees, and the shape of the slice. Sketch a plane that dips 45 degrees, slicing through a cylinder, that produces a cross section that is a different shape – one that is not an ellipse. Sketch the cross section, too. Hint: consider the difference between a can of tuna and a can of soup.

Thomas Hickson, University of St. Thomas, and Ilyse Resnick, University of DelawareSpring, 2015

The shapes of some geological features can be approximated by parts of cylinders. Many slow-moving rivers, for example, have curved beds, and the surface of the river is relatively flat. The remainder of this exercise uses portions of cylinders. You may wish to think of them as idealized river channels.

So far, in this exercise, we have focused on using diagrams and sketches to understand slices through cylinders. Another method for visualizing slices such as these is to use gesture. Believe it or not, research has shown that gesturing helps people to visualize spatial relationships. Here is a short exercise to practice using gesture to visualize slices.

6. The first two diagrams below show a vertical plane slicing perpendicular to a “channel” and people using their hands to gesture the same thing (a vertical plane slicing perpendicular to a “channel”). For each of the other two diagrams, use your own hands to gesture the shape of the “river” bed and the slicing plane.

Thomas Hickson, University of St. Thomas, and Ilyse Resnick, University of DelawareSpring, 2015

Did your gestures look something like these?

7. Consider the “channel” below and figure out how each of the following shapes could be made by slicing through it. You could use gestures to help visualize the slicing plane.

Thomas Hickson, University of St. Thomas, and Ilyse Resnick, University of DelawareSpring, 2015

8. Look at the cross section below. Which channel cut would have this shape?

9. Sketch the other two slices.

10. One last sketch. What would this channel cut look like?

Thomas Hickson, University of St. Thomas, and Ilyse Resnick, University of DelawareSpring, 2015

Any time you are looking at an outcrop that might contain fluvial deposits, look carefully to see whether you can spot any of the shapes from this exercise in the deposits. If so, you may be looking at fluvial channels.

Thomas Hickson, University of St. Thomas, and Ilyse Resnick, University of DelawareSpring, 2015